12 Montecarlo(BP) Final

8/22/2019 12 Montecarlo(BP) Final

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© 2001 ConceptFlow 1

Monte Carlo Analysis




Objectives

By the end of this module, the participant will be able to:• Apply Monte Carlo analysis to business processes.

• Create a Monte Carlo analysis worksheet in MinitabTM.

• Conduct a Monte Carlo simulation using Minitab.

• Apply capability analysis to the output of a Monte Carlo analysis.

• Determine the proper centering and spread of the input variables to

achieve six sigmaTM capability in the output variable.




Why Use Monte Carlo Analysis?

Monte Carlo analysis can be used to:• Estimate the location of a response variable (Y)

• Estimate the variation of a response variable (Y)

• By using information from the input variables (Xs)

• Through use of the transfer function, Y = f(x)




What Is Monte Carlo Analysis?

Monte Carlo analysis:• Generates approximate solutions

• To a variety of practical problems

• Using a computer to perform statistical sampling simulation

experiments.




Minitab Diversion

In order to perform Monte Carlo analysis efficiently in Minitab, it ishelpful to have Minitab automatically update the result column from a

formula. This allows the user to make modifications in the input values

and the output values will be updated without having to re-calculate the

formula.




Minitab: Auto Update of Columns

Minitab can automatically update columns by using the followingprocedure:

1. Selec t (highlight) the input data column headings

2. Choose Edit > Copy Cells

3. Choose Edit > Links > Manage Link s

4. Click Add

5. In Act ion , select Execute commands on ly (last in list)

6. In Commands , type the Y = f(X) formula (begin with Let): for

example: Let Y = X1 + X2

7. Click Add 8. In Manage Link s , click OK

9. The Y column will now automatically update.


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Minitab Auto Update Example

•

As a simple example to illustrate the automatic column update featureof Minitab, we will add two columns together and store the result in a

third column.

• Create a worksheet with input column headings as X1 and X2 and

output column heading as Y. The formula is Y = X1 + X2.



Minitab Example Continued

1. Select (highlight) the input data column headingsIn the worksheet, highlight the X1 and X2 column headings

2. Choose Edit > Copy Cel ls


4. Click Add




5. In Act ion , select Execute commands on ly (last in list)6. In Commands , type the Y = f(X) formula (begin with Let):

for example: Let Y = X1 + X2

7. Click Add




8. In Manage Links, click OK




Monte Carlo Analysis Example

•

In order to illustrate the usefulness of Monte Carlo analysis, we willanalyze an order-entry through order-delivery system.

• Some questions to answer are

1. What is the average time to complete a client order?

2. What is the standard deviation of order completion?

3. What is the capability (in DPM) of the system?

4. What input characteristics are required for a six sigma process?



Monte Carlo Analysis Example

•

The requirement for total time from order entry through order deliveryis 14 days.

• There are five steps to the process:

1. Order entry

2. Manufacturing at site A

3. Ship to site B

4. Manufacturing at site B

5. Ship to client



Process Map for Example

Order

Entry

Mfg at

site A

Ship to

site B

Ship to

client

Mfg at

site B




Data Summary of Process Steps

Data was collected at each process step with the sample

statistics (in days) recorded below:

Step Mean SD Min Max

Order Entry 1.2 0.1 0.9 1.5Mfg at Site A 3.3 0.3 2.4 4.2

Ship to Site B 2.1 0.2 1.5 2.7

Mfg at Site B 3.5 0.4 2.3 4.7

Ship to Client 2.8 0.3 1.9 3.7




Example Continued

Create a worksheet with column headings:• S1 S2 S3 S4 S5 Y




Example Continued

Generate 1000 Normal values for Step 1:• Calc > Random Data > Normal

• Use Mean = 1.2 and Std Dev = .1




Example Continued






Example Continued






Example Continued






Example Continued






Example Continued

Set up the worksheet for automatic column updating:1. Select (highlight) the input data column headings

2. Choose Edit > Copy Cells

3. Choose Edit > Links > Manage Links

4. Click Add

5. In Act ion , select Execute commands on ly (last in list)

6. In Commands , type the Y = f(X) formula (begin with Let):

for example: Let Y = X1 + X2

7. Click Add

8. In Manage Link s , click OK 9. The Y column will now automatically update.




Example Continued

1. Select (highlight) the input data column headingsIn the worksheet, highlight the S1 S2 S3 S4 S5 column headings

2. Choose Edit > Copy Cel ls


4. Click Add




Example Continued

5. In Act ion , select Execute commands on ly (last in list)6. In Commands , type the Y = f(X) formula (begin with Let):

for example: Let Y = S1 + S2 + S3 + S4 + S5

7. Click Add




Example Continued

8. In Manage Links, click OK





Example Continued

The worksheet should appear as below. The values will not be thesame – they are random.




Answering Questions

The first 3 questions can be answered using capability analysis:1. What is the average time to complete a client order?






Capability Analysis

Stat > Quality Tools > Capability Analysis (Normal)




Capability Analysis Output

The output from the Minitab capability analysis is

10 11 12 13 14 15 16

USLUSL

Process Capability Analysis for Y

USL

Target

LSLMean

Sample N

StDev (Within)

StDev (Overall)

Cp

CPU

CPLCpk

Cpm

Pp

PPU

PPL

Ppk

PPM < LSL

PPM > USL

PPM Total

PPM < LSL

PPM > USL

PPM Total

PPM < LSL

PPM > USL

PPM Total

14.0000

*

*12.9067

1000

0.610514

0.610514

*

0.60

*0.60

*

*

0.60

*

0.60

*

28000.00

28000.00

*

36658.52

36658.52

*

36658.52

36658.52

Process Data

Potential (Within) Capability

Overall Capability Observed Performance Exp. "Within" Performance Exp. "Overall" Performance

Within

Overall




Answering Questions 1, 2, 3

1. What is the average time to complete a client order?• Y average is 12.91 days.


• Y standard deviation is 0.61 days


• Y capability is 36,659 DPM




Answering Question 4

4. What input characteristics are required for a six sigma process?• The are at least three ways to answer question 4:

1. Re-center the Step means

2. Reduce the Step standard deviations

3. Re-center the Step means and reduce the Step standard

deviations




Answering Question 4 Continued

If the Step means are re-centered as follows, the capability is near 3.4DPM:

New Original

Step 1 1.0 1.2

Step 2 3.0 3.3

Step 3 2.0 2.1Step 4 3.0 3.5

Step 5 2.2 2.8





8 9 10 11 12 13 14

USLUSL


USL

Target

LSL

Mean

Sample NStDev (Within)

StDev (Overall)

Cp

CPU

CPL

Cpk

Cpm

Pp

PPU

PPL

Ppk

PPM < LSL

PPM > USL

PPM Total

PPM < LSL

PPM > USL

PPM Total

PPM < LSL

PPM > USL

PPM Total

14.0000

*

*

11.1979

10000.639234

0.639234

*

1.46

*

1.46

*

*

1.46

*

1.46

*

0.00

0.00

*

5.84

5.84

*

5.84

5.84

Process Data



Within

Overall





If the Step standard deviations are reduced as follows, the capability isless than 3.4 DPM:

New Original

Step 1 0.1 0.1

Step 2 0.1 0.3

Step 3 0.1 0.2Step 4 0.1 0.4

Step 5 0.1 0.3




12.0 12.5 13.0 13.5 14.0

USLUSL


USL

Target

LSL

Mean

Sample N

StDev (Within)

StDev (Overall)

Cp

CPU

CPL

Cpk

Cpm

Pp

PPU

PPL

Ppk

PPM < LSL

PPM > USL

PPM Total

PPM < LSL

PPM > USL

PPM Total

PPM < LSL

PPM > USL

PPM Total

14.0000

*

*

12.9011

1000

0.224935

0.224935

*

1.63

*

1.63

*

*

1.63

*

1.63

*

0.00

0.00

*

0.52

0.52

*

0.52

0.52

Process Data



Within

Overall






It is typical that the means must be re-centered, along with the standard

deviations being reduced. The following will achieve six sigma

capability:

New Original

Step Mean SD Mean SD

Order Entry 1.0 0.1 1.2 0.1Mfg at Site A 3.0 0.2 3.3 0.3

Ship to Site B 2.1 0.2 2.1 0.2

Mfg at Site B 3.0 0.2 3.5 0.4

Ship to Client 2.7 0.2 2.8 0.3




10 11 12 13 14

USLUSL


USL

Target

LSL

Mean

Sample N

StDev (Within)

StDev (Overall)

Cp

CPU

CPL

Cpk

Cpm

Pp

PPU

PPL

Ppk

PPM < LSL

PPM > USL

PPM Total

PPM < LSL

PPM > USL

PPM Total

PPM < LSL

PPM > USL

PPM Total

14.0000

*

*

11.8088

1000

0.467779

0.467779

*

1.56

*

1.56

*

*

1.56

*

1.56

*

0.00

0.00

*

1.40

1.40

*

1.40

1.40

Process Data



Within

Overall





Class Example

Use Monte Carlo analysis to analyze a call-in order filling system.

• Answer the following questions:








Class Example

The requirement to fill a call-in order is 24 hours.

• There are three steps to the process:

1. Order entry

2. Item collection

3. Ship to client




Process Map for Class Example

CollectItems

Ship toClient

Order Entry




Data Summary of Process Steps

Data was collected at each process step with the sample statistics (in

hours) recorded below:

Step Mean SD Min Max

Order Entry 1.2 0.1 0.9 1.5Item Collection 7.5 0.5 6.0 9.0

Ship to Client 13.5 1.5 9.0 18.0




Class Example

Use Monte Carlo analysis to answer the following questions:








Key Learning Points




Objectives Review

By the end of this module, the participant will be able to:

• Apply Monte Carlo analysis to business processes.

• Create a Monte Carlo analysis worksheet in Minitab.

• Conduct a Monte Carlo simulation using Minitab.

• Apply capability analysis to the output of a Monte Carlo analysis.

• Determine the proper centering and spread of the input variables toachieve six sigma capability in the output variable.



Trademarks and Service Marks

Six Sigma is a federally registered trademark of Motorola, Inc.

Breakthrough Strategy is a federally registered trademark of Six Sigma Academy.

VISION. FOR A MORE PERFECT WORLD is a federally registered trademark of Six Sigma Academy.

ESSENTEQ is a trademark of Six Sigma Academy.

FASTART is a trademark of Six Sigma Academy.

Breakthrough Design is a trademark of Six Sigma Academy.

Breakthrough Lean is a trademark of Six Sigma Academy.

Design with the Power of Six Sigma is a trademark of Six Sigma Academy.

Legal Lean is a trademark of Six Sigma Academy.

SSA Navigator is a trademark of Six Sigma Academy.

SigmaCALC is a trademark of ix Sigma Academy.

SigmaFlow is a trademark of Compass Partners, Inc.

SigmaTRAC is a trademark of DuPont.

MINITAB is a trademark of Minitab, Inc.

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12 Montecarlo(BP) Final